Browsing by Author "Legesse, Hunduma (PhD)"

Now showing 1 - 3 of 3
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    Hermite and Laguerre Differential Equations
    (Addis Ababa University, 2018-09-01) Debela, Oluma; Legesse, Hunduma (PhD)
    In this thesiswe study two important families of polynomials calledHermite and Laguerre polynomials. These special functions, like so many others functions arise as solutions of ordinary differential equations and have many interesting orthogonality properties. We prove some properties of the Hermite and Laguerre polynomials. These polynomials can be given through generating functions and Rodrigues formulae.
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    Solving Dirichlet Problems With Conformal Mappings
    (Addis Ababa University, 2018-08-12) Kassahun, Amnaye; Legesse, Hunduma (PhD)
    In this thesis,given a domain
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    Thesis on Fourier analysis and the Dirichlet problem
    (Addis Ababa University, 2017-09) Yeneabat, Shiferaw; Legesse, Hunduma (PhD)
    In this thesis, using the properties of convergence of Fourier series and some other properties of trigonometric polynomials, in particular that they are sums of holomorphic and anti-holomorphic functions, we are able to solve the Dirichlet problem on the Disc. Then, applying the result for the unit Disc along with a couple of Möbius transformations, we are able to solve the Dirichlet problem on the upper half plane